Donald Trump's Attorney Says Stormy Daniels Agreed No Court Battle, Just Arbitration

President Trump's lawyer, Michael Cohen, insists Stormy Daniels has NO right to drag him or the Prez into court over the "hush" agreement, and he's got that in black and white.

Cohen filed new docs asking the judge to move Stormy's lawsuit from federal court into arbitration ... because he says that's exactly what Stormy agreed to do. Cohen says it's part of the very agreement she's suing to get nullified.

In the docs, Cohen says the ex-porn star herself has admitted to signing the deal in Oct. 2016, and accepting the $130k payment. Although she's making hay about Trump not signing it, Cohen says the document is binding between Stormy and Essential Consultants -- the company Cohen set up to pay her the cash.